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Extensible or expandable garden hoses have become popular. However, their behavior may be surprising to physicists. In this paper, the stress–strain equations that explain this behavior are derived and compared with experiments. The results clearly demonstrate that, since deformation is very large, conventional definitions of strain and stress are not useful and so-called real definitions are needed instead. [ABSTRACT FROM AUTHOR]

Material functions underlie our understanding of rheology. They form the descriptive language of rheologists and require clear definitions. Here, it is shown that the definitions of oscillatory material functions depend on how the oscillating input is mathematically referenced, as a sine or cosine. Depending on this seemingly arbitrary trigonometric reference choice, the (3rd, 7th, 11th, etc.) Fourier coefficients of a nonlinear shear response change sign. Additionally, the even harmonic coefficients of a shear normal stress response are transposed. This impacts large-amplitude oscillatory shear (LAOS) characterization in both shear strain-control (LAOStrain) and shear stress-control (LAOStress) modes. It is important to resolve this issue, because it involves the leading-order nonlinearities and the signs of these higher harmonics convey important information. This paper provides a resolution, in two parts. First, it is shown that the deformation-domain Chebyshev coefficients are immune to the arbitrary trigonometric reference in the time domain, and therefore the Chebyshev-coefficient material functions can be used and interpreted without risk of inconsistency. Second, this paper proposes the convention of referencing to a sine input for strain-control tests (currently the typical convention) and using a cosine input for stress-control (where there is not currently a convention). Finally, clarity is brought to the practical issue of data processing a digital signal, which is required for numerical simulations and every instrument that performs oscillatory characterization. [ABSTRACT FROM AUTHOR]

The creep compliance and relaxation functions used in characterizing the mechanical response of linear viscoelastic solids are traditionally found by conducting two separate experiments. Alternatively, one of the functions may be determined from a single experiment while the other is obtained through interconversion. All direct interconversion methods, however, require the solution of an ill-posed problem. The goal of this paper is to present the theoretical framework for developing a new apparatus, based on “spring loading,” which facilitates the determination of both creep and relaxation functions from a single experiment. There is no need for interconversion. Questions of stability with respect to the measured data are discussed and a stable numerical algorithm is presented. [ABSTRACT FROM AUTHOR]

This paper investigates the transmission loss of symmetric and asymmetric laminate composite panels periodically reinforced by composite stiffeners. A comprehensive model based on periodic structure theory is developed. First order shear deformation theory is used and the coupling of the in-plane motion of the panel with its out-of-plane motion is taken into account. Stiffeners interact with the panel through three forces (two in-plane, one out-of-plane) and a torsion moment. Three types of cross sections are investigated for the composite stiffeners: I-shaped, C-shaped, and omega-shaped cross-sections. The model is validated numerically by comparison with the finite element/boundary element method. Experimental validations are also conducted. In both cases, excellent agreement is obtained. Numerical results show that the in-plane coupling effect is increased by increasing the panel thickness and the stiffener's eccentricity. The in-plane coupling effect is also found to increase with frequency. [ABSTRACT FROM AUTHOR]

A new method for measurement of the viscoelastic properties of the liquid with the torsion resonator on forced resonance is presented in this paper. Both theoretical analysis and experiments of different glycerol-water mixtures with our homemade torsion pendulum apparatus demonstrate that this new method avoids the restriction of the common method that the resonator should have the high quality factor both in air and in liquid sample and has the prominent advantage of measuring the concentrated and large-viscous liquid in the low frequency range (≤100 Hz) with a better precision, which is usually unavailable by the common method. Employment of the new method can thus extend the accessible ranges of viscosity and frequency of the torsion resonator apparatus and close the gaps between conventional rheometers and the torsion resonators. [ABSTRACT FROM AUTHOR]

A three-dimensional lattice Boltzmann method, which couples the color-gradient model for two-phase fluid dynamics with a lattice diffusion-advection scheme for the elastic stress tensor, is developed to study the deformation and breakup of a Newtonian droplet in the Giesekus fluid matrix under simple shear flow. This method is first validated by the simulation of the single-phase Giesekus fluid in a steady shear flow and the droplet deformation in two different viscoelastic fluid systems. It is then used to investigate the effect of Deborah number De , mobility parameter α , and solvent viscosity ratio β on steady-state droplet deformation. We find for 0.025 < α < 0.5 that as De increases, the steady-state droplet deformation decreases until eventually approaching the one in the pure Newtonian case with the viscosity ratio of 1 / β , which is attributed to the strong shear-thinning effect at high De. While for lower α , the droplet deformation exhibits a complex nonmonotonic variation with De. Under constant De , the droplet deformation decreases monotonically with α but increases with β. Force analysis shows that De modifies the droplet deformation by altering the normal viscous and elastic stresses at both poles and equators of the droplet, while α mainly alters the normal stresses at the poles. Finally, we explore the roles of De and α on the critical capillary number C a cr of the droplet breakup. By establishing both Ca – De and Ca – α phase diagrams, we find that the critical capillary number increases with De or α except that a plateau critical capillary number is observed in Ca – De phase diagram. [ABSTRACT FROM AUTHOR]

We modeled flexible microelectronic systems, in which a thinned silicon die is flip-chip bonded to a flexible substrate, and analyzed the stress and strain distribution generated during twisting deformation. Because of the presence of the rigid silicon die, the strain distribution of the system model was significantly different from that of the substrate model. Unlike the substrate model, there is no significant difference in the von Mises strain according to the position in both the molding layer and the substrate in the system model. Therefore, the results of modeling or testing only flexible substrate cannot be directly applied to predict the behavior of flexible microelectronic systems. The copper bumps revealed stress above the ultimate strength as well as the yield strength. Therefore, the copper bump would be the most mechanically weak component in the operation of the face-down flexible microelectronic system during twisting. By replacing copper bumps with polymer bumps, the maximum stress in the bumps can be significantly reduced from 282 to 47 MPa, and the maximum mechanically safe twisting angle was also improved from approximately 40° to 80°. Therefore, in flexible electronic systems where twisting deformation is applied, polymer bumps are a better bonding method than the conventional copper bumps. [ABSTRACT FROM AUTHOR]

A framework for determining the first nonlinear relaxation modulus of a viscoelastic fluid from a medium-amplitude oscillatory shear (MAOS) deformation is constructed. Knowledge of this "MAOS relaxation modulus" allows one to predict the weakly nonlinear stress response of a material under an arbitrary transient deformation via a memory integral expansion. Our framework is demonstrated by explicitly determining the MAOS relaxation modulus for a dilute suspension of Brownian spheroids subject to a dual-frequency oscillatory shear flow. Specifically, we first calculate the second normal stress difference for such a deformation from a corotational memory integral expansion. Second, the microstructural stress response of the model system of Brownian spheroids is determined via a regular perturbation expansion of the orientation distribution function at small dimensionless strain-rate amplitude, or Weissenberg number. An analytical expression for the MAOS relaxation modulus is resolved by comparing the second normal stress difference results of the memory integral expansion and microstructural stress calculation. Finally, using the MAOS relaxation modulus, we reconstruct the stress response of the model system for the start-up and cessation of simple shear and uniaxial extension. In summary, our work offers an approach to utilizing medium (and large) amplitude oscillatory shear results to predict stress dynamics of viscoelastic fluids in other transient, nonlinear flows. [ABSTRACT FROM AUTHOR]

The flow of a two-dimensional foam through a constriction is investigated numerically with the bubble model, and results are compared with existing experimental and numerical studies. We predict the dynamical behavior of the foam by measuring its flowrate as a function of the imposed pressure drop. We show that two flow regimes can be observed, with an affine relationship between flowrate and pressure drop. The model also shows that the flowrate increases with the width of the distribution of bubble sizes. The simulations exhibit a power law dependency of the flowrate in the width of the constriction. The local properties of the flow are also investigated by measuring the velocity field, the frequency and direction of plastic events, and main orientations of strain. We show that the main qualitative features of the plastic and strain tensors fit with existing experiments. Finally, we test a theoretical model that predicts a relationship among plasticity, deformation, and strain. [ABSTRACT FROM AUTHOR]

This work applied a particle-tracking velocimetric technique to observe the deformation field in the die entry pressure-driven extrusion, motivated by insights gained from previous studies of entangled melts in simple shear. Based on several styrene-butadiene rubbers and a polybutadiene melt, we show that shear yielding takes place to result in (shear banding-like) strain localization in the die entry. The degree of strain discontinuity is shown to grow with the level of chain entanglement. The critical pressure for shear yielding corresponds to a level of shear stress at a 45° inclined plane that is comparable to the melt plateau modulus, and therefore can be predicted based on our recent understanding of yielding and strain localization in startup shear. The unstable (i.e., time-dependent) shear strain localization in the die entry during continuous extrusion at a sufficiently high volumetric throughput or pressure results in extrudate distortion that is often also known as gross melt fracture. [ABSTRACT FROM AUTHOR]

Being able to model at what point a yield stress material starts to flow under its own weight is of great importance for many practical applications. However, describing the deformation of yield stress fluids under gravity is anything but a simple exercise due to the feedback between the shape of the deposited material and the locally acting stresses. In this article, we concentrate on a specific aspect of this problem: What is the maximum height of a pile of a yield stress fluid which can be obtained under gravity? For this purpose we use the example of liquid foams in which the yield stress is strongly coupled to the bubble size and the liquid fraction. We show that a good agreement between models and experiments is obtained over a wide parameter range in two limiting cases: When the yield stress is either higher or much lower than the normal stresses encountered in the material. [ABSTRACT FROM AUTHOR]

It has recently been shown that the dynamics of complex interfaces can be treated by hyperelastic finite deformation, and the Cauchy stress tensor can be written as a tensor derivative of the interfacial energy. In the present study, the analytical nature of this tensor derivative was further explored, resulting in a more useful constitutive relation between the stress tensor and the Finger strain tensor. To accommodate the interfacial relaxation effects, an energy balance principle was adopted in developing a nonlinear relaxation model which was then used in a visco-hyperelastic formulation for stress determination. Case studies on this visco-hyperelastic model were performed, and validations against known results were attempted. While at small deformation rates, the new model agrees with the linear viscoelastic calculations, as well as Doi and Ohta's scaling predictions, high nonlinearity was observed at large deformation rates. [ABSTRACT FROM AUTHOR]

Ultra-small electromechanical comb-drive actuators made of GaN crystal were studied in order to apply them to optical micro-electromechanical systems. Using GaN crystals grown on Si substrates by metal-organic chemical vapor deposition, two kinds of electrostatic comb-drive actuators were designed and fabricated. In the fabrication, due to a residual stress of the grown crystal, the movable part of the actuator suffered considerable deformation depending on the growth conditions. The strain-stress issue of the grown crystal layer is discussed on the basis of lattice misfit and thermal expansion. To compensate for a convex deformation, crystallization tension of a thin HfO2 film deposited on a GaN layer was investigated. The displacement of the actuator having dimensions of 52.2 μm in width and 105.4 μm in length was 1.3 μm at 70 V. Several variable systems will be feasible by combining the actuators monolithically with GaN opt-electronic devices. Future applications are also briefly discussed. [ABSTRACT FROM AUTHOR]

A simple method of applying tensile stress to nanomechanical resonators was proposed and demonstrated. Two parallel beams were fabricated by wet etching. The beams then stuck to each other due to surface tension caused by the rinse solution and formed a stiction resonator. The stuck beams were stressed because of the deformation caused by the sticking. The stiction resonators were modeled to estimate the sticking length and evaluate the strain of the resonators. The maximum resonator strain obtained in this study was over 0.3%. The quality factors of the stiction resonators were then experimentally evaluated. Results showed that tensile stress had a significant effect on the quality factor enhancement. Using stiction is an effective, useful, and widely applicable method for the tensile stress application. [ABSTRACT FROM AUTHOR]

The main aim of this work is to study the flow, failure, and rupture dynamics of a benchmark low-density polyethylene (BASF Lupolen 1840H) in true tensile creep conditions in both the viscoelastic and elastic deformation regimes. For this, we used a novel extensional rheometer that for the first time allows real controlled-stress conditions to be applied to the materials (as opposed to nominally controlled-stress) until physical rupture occurs (as opposed to being limited by maximum Hencky strain). We observed that constant strain rate was achieved for all flow conditions, and depending on the level of applied tensile stress, one or two states were obtained. In the former case, the observed mode of rupture was ductile, or liquid-like, and in the latter was cohesive, or elastic-like. The coupling at the molecular level between these flow and rupture mechanisms is not yet fully understood, although some recent studies in the literature may be able to offer at least partial explanations. [ABSTRACT FROM AUTHOR]

This work aims at studying the role of interface properties on the rheological behavior of non-compatibilized and compatibilized polymer blends. Blends of polymethylmetacrylate (PMMA) with polystyrene (PS) and PS functionalized with oxazoline (PSOX) with concentrations of up to 20 w/w of the dispersed phase were used. It was observed that until a critical concentration is reached the increase in PSOX content leads to a significant increase in (a) the elasticity at low frequencies and (b) the relaxation time after cessation of flow, both in shear and extension. This points to a likely significant role played by interface elasticity. Since no chemical reactions occur between PMMA and the oxazoline groups of PSOX, the latter is probably caused by the partial miscibility between PMMA and PSOX. Beyond this critical concentration, the amount of PSOX does not have a significant influence on the rheological behavior of the blends. In order to gain an insight into the relaxation dynamics of the droplets and interface, and their relationship with the rheological behavior of the blends, small angle light scattering (SALS) was used in diluted blends (1 wt % of the dispersed phase) during step shear. SALS shows a slight deformation of dispersed phase in the vorticity direction for the 99PMMA/1PSOX blend while the droplets of the 99PMMA/1PS blend deforms in the flow direction only. This result confirms the large increase in the interfacial elasticity for the 99PMMA/1PSOX blend. [ABSTRACT FROM AUTHOR]

Based on the success of the slotted plate device [Zhu et al., “A slotted plate device for measuring yield stress,” J. Rheol. 45, 1105–1122 (2001)] a numerical analysis is performed for a double concentric cylinder geometry with slotted rotor to measure the yield stress of complex systems such as suspensions. This method overcomes the wall-slip problem, it also takes advantage of the amenable features of commercial rheometers. A finite element model is developed to simulate the deformation and stress distribution in the double concentric cylinder geometry under various wall and material interactions (no-slip, 50% slip, and free slip conditions). Our numerical results show that this geometry greatly reduces the wall slip effect and it proves to be a promising technique for measuring the yield stress of complex systems. [ABSTRACT FROM AUTHOR]

The various aspects of the nonlinear dynamics and stability of nonisothermal film casting process have been investigated solving a two-dimensional (2D) viscoelastic simulation model equipped with the Phan-Thien-Tanner (PTT) constitutive equation by employing a finite element method. This study represents an extension of the earlier report [Kim, Lee, Shin, Jung, and Hyun, J. Non-Newtonian Fluid Mech. 132, 53–60 (2005)] in that two important points are additionally addressed here on the subject: the nonisothermal nature of the film casting, and the differentiation of extension-thickening (strain hardening) and extension-thinning (strain softening) fluids in their different behavior in the film casting process. The PTT model, known for its robustness in portraying dynamics in the extensional deformation processes which include the film casting of this study along with film blowing and fiber spinning as well, renders the transient and steady state solutions of the dynamics in the 2D, viscoelastic, nonisothermal, film casting capable of explaining the effects of various process and material parameters of the system on the film dynamics of the process. Especially, the different behavior displayed by two polymer groups, i.e., the extension-thickening low density polyethylene (LDPE) type and the extension-thinning high density polyethylene (HDPE) type, in the film casting can be readily explained by the PTT equation-included simulation model. The three nonlinear phenomena commonly observed in film casting, i.e., draw resonance oscillation, edge bead, and neck-in, have been successfully delineated in this study using the simulation and experimental results. [ABSTRACT FROM AUTHOR]

The bulk viscosity of a suspension is defined analogous to that for a pure fluid as the constant of proportionality relating the deviation of the trace of the macroscopic stress from its equilibrium value to the average rate of expansion. In a suspension the equilibrium macroscopic stress is the sum of the thermodynamic pressure of the fluid and the osmotic pressure of the suspended particles. Rigid particles suspended in an expanding fluid cause a disturbance flow that contributes to the total mechanical pressure in the system, thereby changing the effective bulk viscosity. Expressions are derived to compute the effective bulk viscosity for all concentrations and all expansion rates for a system of rigid particles suspended in a uniformly expanding fluid. The expansion flow drives the suspension microstructure out of equilibrium and the thermal motion of the particles tries to restore the equilibrium. The Péclet number, defined as the expansion rate made dimensionless with the Brownian time scale, governs the departure of the microstructure from equilibrium. The contribution to bulk viscosity is determined to second order in volume fraction of particles for all compression rates (all negative Péclet numbers). A “compression thickening” of the suspension is observed at large compression rates. [ABSTRACT FROM AUTHOR]

A finite simple shear deformation of an elastic solid induces unequal normal stresses. This nonlinear phenomenon, known as the Poynting effect, is governed by a universal relation between shear strain and first normal stresses difference, valid for nondissipative isotropic elastic materials. We provide the first experimental evidence that an analog of the Poynting effect exists in aqueous foams where, besides the elastic stress, there are significant viscous or plastic stresses. These results are interpreted in the framework of a constitutive model, derived from a physical description of foam rheology. [ABSTRACT FROM AUTHOR]

The stress relaxation behavior of a well-entangled polystyrene following step shear deformations is investigated. New experimental data are reported for the relaxation of shear stress and first normal stress difference that are not affected by imperfect strain history or transducer compliance. Anomalous (type C) shear stress relaxation behavior is observed indicating significant discrepancies from the tube model prediction for the damping function. First normal stress difference data are used to evaluate the Lodge-Meissner relation and small deviations are observed. We find that slip between the test fluid and cone-and-plate fixtures is responsible for the observed type C behavior, but only leads to small departures from the Lodge-Meissner relation. Simulations of step strain flows with wall slip show qualitative agreement with experimental results. In addition, we examine the issue of polydispersity in the polystyrene standards used to prepare well-entangled solutions for this and similar studies. [ABSTRACT FROM AUTHOR]

Slip occurs at the interfaces between immiscible polymer melts at high shear stress. We demonstrate that this reduces adhesion during coextrusion. A 20-layer polystyrene (PS)/poly(methyl methacrylate) (PMMA) alternating layer sample was coextruded and the adhesion at each internal interface was measured with the asymmetric dual cantilever beam crack propagation test. When the shear stress experienced by an interface is low, interfacial slip is negligible and interfacial adhesion is high, comparable to a laminated interface. When the shear stress exceeds a critical value, interfacial slip begins to develop and interfacial adhesion begins to decrease with shear stress. Above another critical stress, full slip has been developed at the interface and adhesion reaches a plateau value, which is about 1/3 of the equilibrium value. The changes in adhesion versus shear stress follow a master curve for different flow rates. This supports the hypothesis that polymer chains at the interface are disentangled by the shear stress during coextrusion. It was also found that annealing restored adhesion on the reptation time scale indicating that entanglements were reestablished at the interface. Creating block copolymer by a coupling reaction at the interface during coextrusion increased adhesion to level even higher than the laminated interface. [ABSTRACT FROM AUTHOR]

Effects of inertia on the rheology of dilute Newtonian emulsion of drops in shear flow are investigated using direct numerical simulation. The drop shape and flow are computed by solving the Navier-Stokes equation in two phases using Front-tracking method. Effective stress is computed using Batchelor’s formulation, where the interfacial stress is obtained from the simulated drop shape and the perturbation stress from the velocity field. At low Reynolds number, the simulation shows good agreement with various analytical results and experimental measurements. At higher inertia deformation is enhanced and the tilt angle of the drop becomes larger than forty-five degree. The inertial morphology directly affects interfacial stresses. The first and the second interfacial normal stress differences are found to change sign due to the change in drop orientation. The interfacial shear stress is enhanced by inertia and decreases with capillary number at lower inertia but increases at higher inertia. The total excess stresses including perturbation stress contribution shows similar patterns. [ABSTRACT FROM AUTHOR]